8 papers
Aspects of deformation invariance of plurigenera of Kähler varieties
Jiawei Feng, Yi Li, Sheng Rao
We study several aspects of deformation invariance of plurigenera in Kähler families over a smooth curve. First, for a relatively flat coherent sheaf, we characterize local constan…
Matsumura's extension problem for pluricanonical forms in Kähler families I: the smooth and essentially Moishezon cases
Jian Chen, Sheng Rao, Kai Wang
In this paper, we study a problem posed by Matsumura on the extension of pluricanonical forms in Kähler families with a relatively nef canonical bundle. We give an affirmative answ…
Bimeromorphic invariance of -property and blow-up formulae I: counterexamples and derived category approach
Wei Liu, Sheng Rao
Using N. Honda's construction of twistor spaces, bimeromorphic invarince of -lemma for threefolds and embedded resolution, we find a smooth compact complex th…
Deformation invariance of canonical nefness in smooth Kahler morphisms
Mu-Lin Li, Xiao-Lei Liu, Sheng Rao
Let be a smooth Kähler morphism from complex manifold to the unit disc. We prove that the canonical bundle is nef for \emph{every} fiber as soon as it…
On Pseudo-Effectivity and Volumes of Adjoint Classes in Kähler Families with Projective Central Fiber
Christopher D. Hacon, Yi Li, Sheng Rao
This paper is devoted to studying the deformation behavior of pseudo-effective canonical divisors and volumes of adjoint classes in Kähler families. Based on recent developments in…
Deformation of nef adjoint canonical line bundles
Mu-Lin Li, Sheng Rao, Kai Wang
Much inspired by J. A. Wiśniewski's nef-value function method, we prove that in a smooth projective family over the unit disk, if the adjoint bundle of the canonical line bundle wi…
Rigidity for compact hyperbolic complex manifolds
Mu-Lin Li, Sheng Rao, Mengjiao Wang
We study the deformation behavior of compact hyperbolic complex manifolds. Let be a smooth family of compact complex manifolds over the unit disk in $\…
Upper semicontinuity of algebraic dimension
Mu-Lin Li, Sheng Rao, Kai Wang +1
We prove the conjecture that the deformation limit of Moishezon manifolds under a smooth deformation over the unit disc in is Moishezon. More generally, for a proper h…